Maximum Valency Lattice Gas Models

We study lattice gas models with the imposition of a constraint on the maximum number of bonds (nearest neighbor interactions) that particles can participate in. The critical parameters, as well as the coexistence region are studied using the mean field approximation and the Bethe-Peierls approximation. We find that the reduction of the number of interactions suppresses the temperature-density region where the liquid and gas phases coexist. We confirm these results from simulations using the histogram reweighting method employing grand Canonical Monte Carlo simulations

New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponential growth of its fundamental group, which translates in string theory to a higher effective central charge arising from winding strings. This exponential density of winding modes is related by modular invariance to the infrared small perturbation spectrum. Using self-consistent approximations valid at large radius, we analyze this correspondence explicitly in a broad set of time-dependent solutions, finding precise agreement between the effective central charge and the corresponding infrared small perturbation spectrum. This indicates a basic relation between geometry, topology, and dimensionality in string theory.Comment: 28 pages, harvmac big. v2: references and KITP preprint number added, minor change

Configurational Entropy and Diffusivity of Supercooled Water

We calculate the configurational entropy S_conf for the SPC/E model of water for state points covering a large region of the (T,rho) plane. We find that (i) the (T,rho) dependence of S_conf correlates with the diffusion constant and (ii) that the line of maxima in S_conf tracks the line of density maxima. Our simulation data indicate that the dynamics are strongly influenced by S_conf even above the mode-coupling temperature T_MCT(rho).Comment: Significant update of reference

Transitions between Inherent Structures in Water

The energy landscape approach has been useful to help understand the dynamic properties of supercooled liquids and the connection between these properties and thermodynamics. The analysis in numerical models of the inherent structure (IS) trajectories -- the set of local minima visited by the liquid -- offers the possibility of filtering out the vibrational component of the motion of the system on the potential energy surface and thereby resolving the slow structural component more efficiently. Here we report an analysis of an IS trajectory for a widely-studied water model, focusing on the changes in hydrogen bond connectivity that give rise to many IS separated by relatively small energy barriers. We find that while the system \emph{travels} through these IS, the structure of the bond network continuously modifies, exchanging linear bonds for bifurcated bonds and usually reversing the exchange to return to nearly the same initial configuration. For the 216 molecule system we investigate, the time scale of these transitions is as small as the simulation time scale ($\approx 1$ fs). Hence for water, the transitions between each of these IS is relatively small and eventual relaxation of the system occurs only by many of these transitions. We find that during IS changes, the molecules with the greatest displacements move in small ``clusters'' of 1-10 molecules with displacements of $\approx 0.02-0.2$ nm, not unlike simpler liquids. However, for water these clusters appear to be somewhat more branched than the linear ``string-like'' clusters formed in a supercooled Lennar d-Jones system found by Glotzer and her collaborators.Comment: accepted in PR

Instantaneous Normal Mode Analysis of Supercooled Water

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by the mode-coupling theory. We find, surprisingly, that the diffusion constant depends mainly on the fraction of directions in configuration space connecting different local minima, supporting the conjecture that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find an unexpected relation between the number of basins accessed in equilibrium and the connectivity between them.Comment: 5 pages, 4 figure

Thermodynamic and structural aspects of the potential energy surface of simulated water

Relations between the thermodynamics and dynamics of supercooled liquids approaching a glass transition have been proposed over many years. The potential energy surface of model liquids has been increasingly studied since it provides a connection between the configurational component of the partition function on one hand, and the system dynamics on the other. This connection is most obvious at low temperatures, where the motion of the system can be partitioned into vibrations within a basin of attraction and infrequent inter-basin transitions. In this work, we present a description of the potential energy surface properties of supercooled liquid water. The dynamics of this model has been studied in great details in the last years. Specifically, we locate the minima sampled by the liquid by ``quenches'' from equilibrium configurations generated via molecular dynamics simulations. We calculate the temperature and density dependence of the basin energy, degeneracy, and shape. The temperature dependence of the energy of the minima is qualitatively similar to simple liquids, but has anomalous density dependence. The unusual density dependence is also reflected in the configurational entropy, the thermodynamic measure of degeneracy. Finally, we study the structure of simulated water at the minima, which provides insight on the progressive tetrahedral ordering of the liquid on cooling

Computer-vision based method for quantifying rising from chair in Parkinson's disease patients

BACKGROUND: The ability to arise from a sitting to a standing position is often impaired in Parkinson's disease (PD). This impairment is associated with an increased risk of falling, and higher risk of dementia. We propose a novel approach to estimate Movement Disorder Society Unified PD Rating Scale (MDS-UPDRS) ratings for “item 3.9” (arising from chair) using a computer vision-based method, whereby we use clinically informed reasoning to engineer a small number of informative features from high dimensional markerless pose estimation data. METHODS: We analysed 447 videos collected via the KELVIN-PD™ platform, recorded in clinical settings at multiple sites, using commercially available mobile smart devices. Each video showed an examination for item 3.9 of the MDS-UPDRS and had an associated severity rating from a trained clinician on the 5-point scale (0, 1, 2, 3 or 4). The deep learning library OpenPose was used to extract pose estimation key points from each frame of the videos, resulting in time-series signals for each key point. From these signals, features were extracted which capture relevant characteristics of the movement; velocity variation, smoothness, whether the patient used their hands to push themselves up, how stooped the patient was while sitting and how upright the patient was when fully standing. These features were used to train an ordinal classification system (with one class for each of the possible ratings on the UPDRS), based on a series of random forest classifiers. RESULTS: The UPDRS ratings estimated by this system, using leave-one-out cross validation, corresponded exactly to the ratings made by clinicians in 79% of videos, and were within one of those made by clinicians in 100% of cases. The system was able to distinguish normal from Parkinsonian movement with a sensitivity of 62.8% and a specificity of 90.3%. Analysis of misclassified examples highlighted the potential of the system to detect potentially mislabelled data. CONCLUSION: We show that our computer-vision based method can accurately quantify PD patients’ ability to perform the arising from chair action. As far as we are aware this is the first study estimating scores for item 3.9 of the MDS-UPDRS from singular monocular video. This approach can help prevent human error by identifying unusual clinician ratings, and provides promise for such a system being used routinely for clinical assessments, either locally or remotely, with potential for use as stratification and outcome measures in clinical trials

Collaborative Evolution of a Dynamic Scenario Model for the Interaction of Critical Infrastructures

ABSTRACT This paper reviews current work on a model of the cascading effects of Critical Infrastructure (CI) failures during disasters. Based upon the contributions of 26 professionals, we have created a reliable model for the interaction among sixteen CIs. An internal CI model can be used as a core part of a number of larger models, each of which are tailored to a specific disaster in a specific location

Equilibration times in numerical simulation of structural glasses: Comparing parallel tempering and conventional molecular dynamics

Generation of equilibrium configurations is the major obstacle for numerical investigation of the slow dynamics in supercooled liquid states. The parallel tempering (PT) technique, originally proposed for the numerical equilibration of discrete spin-glass model configurations, has recently been applied in the study of supercooled structural glasses. We present an investigation of the ability of parallel tempering to properly sample the liquid configuration space at different temperatures, by mapping the PT dynamics into the dynamics of the closest local potential energy minima (inherent structures). Comparing the PT equilibration process with the standard molecular dynamics equilibration process we find that the PT does not increase the speed of equilibration of the (slow) configurational degrees of freedom.Comment: 5 pages, 3 figure